Pub Date : 2023-08-28DOI: 10.56754/0719-0646.2502.289
A. Ghandouri, H. Mejjaoli, S. Omri
We define and study the Hardy spaces associated with singular partial differential operators. Also, a characterization by mean of atomic decomposition is investigated.
我们定义并研究了与奇异偏微分算子相关的Hardy空间。此外，还研究了原子分解的表征方法。
{"title":"On generalized Hardy spaces associated with singular partial differential operators","authors":"A. Ghandouri, H. Mejjaoli, S. Omri","doi":"10.56754/0719-0646.2502.289","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.289","url":null,"abstract":"We define and study the Hardy spaces associated with singular partial differential operators. Also, a characterization by mean of atomic decomposition is investigated.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46750227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.56754/0719-0646.2502.273
Mehdi Dehghanian, Choonkill Park, Y. Sayyari
In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the $(alpha,beta)$-functional inequality: begin{align*} &Vert mathcal{F}(x+y+z)-mathcal{F}(x+z)-mathcal{F}(y-x+z)-mathcal{F}(x-z)Vert nonumber &leq Vert alpha (mathcal{F}(x+y-z)+mathcal{F}(x-z)-mathcal{F}(y))Vert + Vert beta (mathcal{F}(x-z) &+mathcal{F}(x)-mathcal{F}(z))Vert end{align*} where $alpha$ and $beta$ are fixed nonzero complex numbers with $vertalpha vert +vert beta vert<2$ by using the fixed point method.
{"title":"Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem","authors":"Mehdi Dehghanian, Choonkill Park, Y. Sayyari","doi":"10.56754/0719-0646.2502.273","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.273","url":null,"abstract":"In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the $(alpha,beta)$-functional inequality: begin{align*} &Vert mathcal{F}(x+y+z)-mathcal{F}(x+z)-mathcal{F}(y-x+z)-mathcal{F}(x-z)Vert nonumber &leq Vert alpha (mathcal{F}(x+y-z)+mathcal{F}(x-z)-mathcal{F}(y))Vert + Vert beta (mathcal{F}(x-z) &+mathcal{F}(x)-mathcal{F}(z))Vert end{align*} where $alpha$ and $beta$ are fixed nonzero complex numbers with $vertalpha vert +vert beta vert<2$ by using the fixed point method.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43820847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-07DOI: 10.56754/0719-0646.2502.251
P. Eloe, Jeffrey T. Neugebauer
It has been shown that, under suitable hypotheses, boundary value problems of the form, $Ly+lambda y=f,$ $BC y =0$ where $L$ is a linear ordinary or partial differential operator and $BC$ denotes a linear boundary operator, then there exists $Lambda >0$ such that $fge 0$ implies $lambda y ge 0$ for $lambdain [-Lambda ,Lambda ]setminus{0},$ where $y$ is the unique solution of $Ly+lambda y=f,$ $BC y =0$. So, the boundary value problem satisfies a maximum principle for $lambdain [-Lambda ,0)$ and the boundary value problem satisfies an anti-maximum principle for $lambdain (0, Lambda ]$. In an abstract result, we shall provide suitable hypotheses such that boundary value problems of the form, $D_{0}^{alpha}y+beta D_{0}^{alpha -1}y=f,$ $BC y =0$ where $D_{0}^{alpha}$ is a Riemann-Liouville fractional differentiable operator of order $alpha$, $10$ such that $fge 0$ implies $beta D_{0}^{alpha -1}y ge 0$ for $beta in [-mathcal{B} ,mathcal{B} ]setminus{0},$ where $y$ is the unique solution of $D_{0}^{alpha}y+beta D_{0}^{alpha -1}y =f,$ $BC y =0$. Two examples are provided in which the hypotheses of the abstract theorem are satisfied to obtain the sign property of $beta D_{0}^{alpha -1}y.$ The boundary conditions are chosen so that with further analysis a sign property of $beta y$ is also obtained. One application of monotone methods is developed to illustrate the utility of the abstract result.
{"title":"Maximum, anti-maximum principles and monotone methods for boundary value problems for Riemann-Liouville fractional differential equations in neighborhoods of simple eigenvalues","authors":"P. Eloe, Jeffrey T. Neugebauer","doi":"10.56754/0719-0646.2502.251","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.251","url":null,"abstract":"It has been shown that, under suitable hypotheses, boundary value problems of the form, $Ly+lambda y=f,$ $BC y =0$ where $L$ is a linear ordinary or partial differential operator and $BC$ denotes a linear boundary operator, then there exists $Lambda >0$ such that $fge 0$ implies $lambda y ge 0$ for $lambdain [-Lambda ,Lambda ]setminus{0},$ where $y$ is the unique solution of $Ly+lambda y=f,$ $BC y =0$. So, the boundary value problem satisfies a maximum principle for $lambdain [-Lambda ,0)$ and the boundary value problem satisfies an anti-maximum principle for $lambdain (0, Lambda ]$. In an abstract result, we shall provide suitable hypotheses such that boundary value problems of the form, $D_{0}^{alpha}y+beta D_{0}^{alpha -1}y=f,$ $BC y =0$ where $D_{0}^{alpha}$ is a Riemann-Liouville fractional differentiable operator of order $alpha$, $1<alpha le 2$, and $BC$ denotes a linear boundary operator, then there exists $mathcal{B} >0$ such that $fge 0$ implies $beta D_{0}^{alpha -1}y ge 0$ for $beta in [-mathcal{B} ,mathcal{B} ]setminus{0},$ where $y$ is the unique solution of $D_{0}^{alpha}y+beta D_{0}^{alpha -1}y =f,$ $BC y =0$. Two examples are provided in which the hypotheses of the abstract theorem are satisfied to obtain the sign property of $beta D_{0}^{alpha -1}y.$ The boundary conditions are chosen so that with further analysis a sign property of $beta y$ is also obtained. One application of monotone methods is developed to illustrate the utility of the abstract result.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43858847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-05DOI: 10.56754/0719-0646.2502.231
A. Bensalem, Abdelkrim Salim, B. Ahmad, M. Benchohra
In this paper, we investigate existence of mild solutions to a non-instantaneous integrodifferential equation via resolvent operators in the sense of Grimmer in Fréchet spaces. Utilizing the technique of measures of noncompactness in conjunction with the Darbo's fixed point theorem, we present sufficient criteria ensuring the controllability of the given problem. An illustrative example is also discussed.
{"title":"Existence and controllability of integrodifferential equations with non-instantaneous impulses in Fréchet spaces","authors":"A. Bensalem, Abdelkrim Salim, B. Ahmad, M. Benchohra","doi":"10.56754/0719-0646.2502.231","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.231","url":null,"abstract":"In this paper, we investigate existence of mild solutions to a non-instantaneous integrodifferential equation via resolvent operators in the sense of Grimmer in Fréchet spaces. Utilizing the technique of measures of noncompactness in conjunction with the Darbo's fixed point theorem, we present sufficient criteria ensuring the controllability of the given problem. An illustrative example is also discussed.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44889535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-04DOI: 10.56754/0719-0646.2502.211
Sahar M. A. Maqbol, R. S. Jain, B. Reddy
This article aims to examine the existence and Hyers-Ulam stability of non-local random impulsive neutral stochastic integrodifferential delayed equations with Poisson jumps. Initially, we prove the existence of mild solutions to the equations by using the Banach fixed point theorem. Then, we investigate stability via the continuous dependence of solutions on the initial value. Next, we study the Hyers-Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, we give an illustrative example of our main result.
{"title":"On stability of nonlocal neutral stochastic integro differential equations with random impulses and Poisson jumps","authors":"Sahar M. A. Maqbol, R. S. Jain, B. Reddy","doi":"10.56754/0719-0646.2502.211","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.211","url":null,"abstract":"This article aims to examine the existence and Hyers-Ulam stability of non-local random impulsive neutral stochastic integrodifferential delayed equations with Poisson jumps. Initially, we prove the existence of mild solutions to the equations by using the Banach fixed point theorem. Then, we investigate stability via the continuous dependence of solutions on the initial value. Next, we study the Hyers-Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, we give an illustrative example of our main result.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49215480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.56754/0719-0646.2502.331
E. Ballico
Let $Xsubset PP^r$ be an integral projective variety. We study the dimensions of the joins of several copies of the osculating varieties $J(X,m)$ of $X$. Our methods are general, but we give a full description in all cases only if $X$ is a linearly normal embedding of $PP^1times PP^1$. For these embeddings of $PP^1times PP^1$ we give several examples and then study the joins of one copy of $J(X,m)$ and an arbitrary number of copies of $X$.
{"title":"Osculating varieties and their joins: $mathbb{P}^1times mathbb{P}^1$","authors":"E. Ballico","doi":"10.56754/0719-0646.2502.331","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.331","url":null,"abstract":"Let $Xsubset PP^r$ be an integral projective variety. We study the dimensions of the joins of several copies of the osculating varieties $J(X,m)$ of $X$. Our methods are general, but we give a full description in all cases only if $X$ is a linearly normal embedding of $PP^1times PP^1$. For these embeddings of $PP^1times PP^1$ we give several examples and then study the joins of one copy of $J(X,m)$ and an arbitrary number of copies of $X$.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41427504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.56754/0719-0646.2502.321
F. Soltani, Slim Ben Rejeb
In this work, by combining Carlson-type and Nash-type inequalities for the Weinstein transform $mathscr{F}_W$ on $mathbb{K}=mathbb{R}^{d-1}times[0,infty)$, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also local-type uncertainty inequalities for the Weinstein transform $mathscr{F}_W$, and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.
{"title":"Laeng-Morpurgo-type uncertainty inequalities for the Weinstein transform","authors":"F. Soltani, Slim Ben Rejeb","doi":"10.56754/0719-0646.2502.321","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.321","url":null,"abstract":"In this work, by combining Carlson-type and Nash-type inequalities for the Weinstein transform $mathscr{F}_W$ on $mathbb{K}=mathbb{R}^{d-1}times[0,infty)$, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also local-type uncertainty inequalities for the Weinstein transform $mathscr{F}_W$, and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45178958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-19DOI: 10.56754/0719-0646.2502.195
S. Dragomir, S. S. Dragomir
For a continuous and positive function (wleft( lambda right) ,) (lambda>0) and (mu ) a positive measure on ((0,infty )) we consider the following Integral Transform [ begin{equation*} mathcal{D}left( w,mu right) left( Tright) :=int_{0}^{infty }wleft(lambda right) left( lambda +Tright)^{-1}dmu left( lambda right) , end{equation*} ] where the integral is assumed to exist for (T) a postive operator on a complex Hilbert space (H). We show among others that, if ( beta geq A geq alpha > 0, , B > 0 ) with ( M geq B-A geq m > 0 ) for some constants ( alpha, beta, m, M ), then [ begin{align*} 0 & leq frac{m^{2}}{M^{2}}left[ mathcal{D}left( w,mu right) left(betaright) - mathcal{D}left( w,mu right) left(M+betaright) right] & leq frac{m^{2}}{M}left[ mathcal{D}left( w,mu right) left(betaright) - mathcal{D}left( w,mu right) left(M+betaright) right] left( B-Aright)^{-1} & leq mathcal{D}left( w,mu right) left(Aright) - mathcal{D}left(w,muright) left(Bright) & leq frac{M^{2}}{m}left[ mathcal{D}left( w,mu right) left(alpharight) - mathcal{D}left( w,mu right) left(m+alpharight) right] left(B-Aright)^{-1} & leq frac{M^{2}}{m^{2}}left[ mathcal{D}left( w,mu right) left(alpharight) - mathcal{D}left( w,mu right) left(m+alpharight) right]. end{align*} ] Some examples for operator monotone and operator convex functions as well as for integral transforms (mathcal{D}left( cdot ,cdot right) ) related to the exponential and logarithmic functions are also provided.
{"title":"Several inequalities for an integral transform of positive operators in Hilbert spaces with applications","authors":"S. Dragomir, S. S. Dragomir","doi":"10.56754/0719-0646.2502.195","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.195","url":null,"abstract":"For a continuous and positive function (wleft( lambda right) ,) (lambda>0) and (mu ) a positive measure on ((0,infty )) we consider the following Integral Transform [ begin{equation*} mathcal{D}left( w,mu right) left( Tright) :=int_{0}^{infty }wleft(lambda right) left( lambda +Tright)^{-1}dmu left( lambda right) , end{equation*} ] where the integral is assumed to exist for (T) a postive operator on a complex Hilbert space (H). We show among others that, if ( beta geq A geq alpha > 0, , B > 0 ) with ( M geq B-A geq m > 0 ) for some constants ( alpha, beta, m, M ), then [ begin{align*} 0 & leq frac{m^{2}}{M^{2}}left[ mathcal{D}left( w,mu right) left(betaright) - mathcal{D}left( w,mu right) left(M+betaright) right] & leq frac{m^{2}}{M}left[ mathcal{D}left( w,mu right) left(betaright) - mathcal{D}left( w,mu right) left(M+betaright) right] left( B-Aright)^{-1} & leq mathcal{D}left( w,mu right) left(Aright) - mathcal{D}left(w,muright) left(Bright) & leq frac{M^{2}}{m}left[ mathcal{D}left( w,mu right) left(alpharight) - mathcal{D}left( w,mu right) left(m+alpharight) right] left(B-Aright)^{-1} & leq frac{M^{2}}{m^{2}}left[ mathcal{D}left( w,mu right) left(alpharight) - mathcal{D}left( w,mu right) left(m+alpharight) right]. end{align*} ] Some examples for operator monotone and operator convex functions as well as for integral transforms (mathcal{D}left( cdot ,cdot right) ) related to the exponential and logarithmic functions are also provided.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48523841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-19DOI: 10.56754/0719-0646.2502.173
A. Zerki, K. Bachouche, K. Ait-Mahiout
In this paper, we consider the following ((n+1))st order bvp on the half line with a (phi-)Laplacian operator [ begin{cases} (phi(u^{(n)}))'(t) = f(t,u(t),ldots,u^{(n)}(t)), & text{a.e.},, tin [0,+infty), n in mathbb{N}setminus{0}, u^{(i)}(0) = A_{i}, , i=0,ldots,n-2, u^{(n-1)}(0) + au^{(n)}(0) = B, u^{(n)}(+infty) = C. end{cases} ] The existence of solutions is obtained by applying Schaefer's fixed point theorem under a one-sided Nagumo condition with nonordered lower and upper solutions method where (f) is a (L^{1})-Carathéodory function.
本文用(phi-)拉普拉斯算子[ begin{cases} (phi(u^{(n)}))'(t) = f(t,u(t),ldots,u^{(n)}(t)), & text{a.e.},, tin [0,+infty), n in mathbb{N}setminus{0}, u^{(i)}(0) = A_{i}, , i=0,ldots,n-2, u^{(n-1)}(0) + au^{(n)}(0) = B, u^{(n)}(+infty) = C. end{cases} ]考虑了半线上的((n+1)) st阶bvp问题，在具有无序上下解方法的单侧Nagumo条件下，应用Schaefer不动点定理，得到了该问题解的存在性，其中(f)为(L^{1}) - carathacimodory函数。
{"title":"Existence of solutions for higher order $phi-$Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions","authors":"A. Zerki, K. Bachouche, K. Ait-Mahiout","doi":"10.56754/0719-0646.2502.173","DOIUrl":"https://doi.org/10.56754/0719-0646.2502.173","url":null,"abstract":"In this paper, we consider the following ((n+1))st order bvp on the half line with a (phi-)Laplacian operator [ begin{cases} (phi(u^{(n)}))'(t) = f(t,u(t),ldots,u^{(n)}(t)), & text{a.e.},, tin [0,+infty), n in mathbb{N}setminus{0}, u^{(i)}(0) = A_{i}, , i=0,ldots,n-2, u^{(n-1)}(0) + au^{(n)}(0) = B, u^{(n)}(+infty) = C. end{cases} ] The existence of solutions is obtained by applying Schaefer's fixed point theorem under a one-sided Nagumo condition with nonordered lower and upper solutions method where (f) is a (L^{1})-Carathéodory function.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44413330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-20DOI: 10.56754/0719-0646.2501.057
Mudasir Younis, Nikola Mirkov, A. Savić, M. Pantović, S. Radenović
This paper aims to correct recent results on a generalized class of $digamma-$contractions in the context of $b-$metric spaces. The significant work consists of repairing some novel results involving $digamma-$contraction within the structure of $b$-metric spaces. Our objective is to take advantage of the property $(F1)$ instead of the four properties viz. $(F1)$, $(F2)$, $(F3)$ and $(F4)$ applied in the results of Nazam textit{et al.} [``Coincidence and common fixed point theorems for four mappings satisfying $(alpha_s,F)-$contraction", Nonlinear Anal: Model. Control., vol. 23, no. 5, pp. 664--690, 2018]. Our approach of proving the results utilizing only the condition $(F1)$ enriches, improves, and condenses the proofs of a multitude of results in the existing state-of-art.
{"title":"Some critical remarks on recent results concerning $digamma-$contractions in $b$-metric spaces","authors":"Mudasir Younis, Nikola Mirkov, A. Savić, M. Pantović, S. Radenović","doi":"10.56754/0719-0646.2501.057","DOIUrl":"https://doi.org/10.56754/0719-0646.2501.057","url":null,"abstract":"This paper aims to correct recent results on a generalized class of $digamma-$contractions in the context of $b-$metric spaces. The significant work consists of repairing some novel results involving $digamma-$contraction within the structure of $b$-metric spaces. Our objective is to take advantage of the property $(F1)$ instead of the four properties viz. $(F1)$, $(F2)$, $(F3)$ and $(F4)$ applied in the results of Nazam textit{et al.} [``Coincidence and common fixed point theorems for four mappings satisfying $(alpha_s,F)-$contraction\", Nonlinear Anal: Model. Control., vol. 23, no. 5, pp. 664--690, 2018]. Our approach of proving the results utilizing only the condition $(F1)$ enriches, improves, and condenses the proofs of a multitude of results in the existing state-of-art.","PeriodicalId":36416,"journal":{"name":"Cubo","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43315555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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