Z. Hammouch, Anam Zahra, Aziz Ur Rehman, S. A. Mardan
{"title":"AN EFFICIENT NUMERICAL TECHNIQUE FOR SOLVING HEAT EQUATION WITH NONLOCAL BOUNDARY CONDITIONS","authors":"Z. Hammouch, Anam Zahra, Aziz Ur Rehman, S. A. Mardan","doi":"10.31197/atnaa.846217","DOIUrl":"https://doi.org/10.31197/atnaa.846217","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72974954","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}
In this note we show the somewhat surprising fact that the proof of the `if part' of the distinguished characterizations of metric completeness due to Kirk, and Suzuki and Takahashi, respectively, can be deduced in a straightforward manner from Hu's theorem that a metric space is complete if and only if any Banach contraction on bounded and closed subsets thereof has a fixed point. We also take advantage of this approach to easily deduce a characterization of metric completeness via fixed point theorems for $alpha -psi $-contractive mappings.
{"title":"Hu's characterization of metric completeness revisited","authors":"Salvador ROMAGUERA BONİLLA","doi":"10.31197/atnaa.1090077","DOIUrl":"https://doi.org/10.31197/atnaa.1090077","url":null,"abstract":"In this note we show the somewhat surprising fact that the proof of the `if part' of the distinguished characterizations of metric completeness due to Kirk, and Suzuki and Takahashi, respectively, can be deduced in a straightforward manner from Hu's theorem that a metric space is complete if and only if any Banach contraction on bounded and closed subsets thereof has a fixed point. We also take advantage of this approach to easily deduce a characterization of metric completeness via fixed point theorems for $alpha -psi $-contractive mappings.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"136 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77706618","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}
{"title":"Existence results for nonlocal Cauchy problem of nonlinear $psi-$Caputo type fractional differential equations via topological degree methods","authors":"Ali El Mfadel, S. Melliani, Elomari M'hamed","doi":"10.31197/atnaa.1059793","DOIUrl":"https://doi.org/10.31197/atnaa.1059793","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79283167","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}
{"title":"Some new equivalents of the Brouwer fixed point theorem","authors":"Sehie Park","doi":"10.31197/atnaa.1086232","DOIUrl":"https://doi.org/10.31197/atnaa.1086232","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89136835","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}
Zipper fractal interpolation function (ZFIF) is a generalization of fractal interpolation function through an improved version of iterated function system by using a binary parameter called a signature. The signature allows the horizontal scalings to be negative. ZFIFs have a complex geometric structure, and they can be non-differentiable on a dense subset of an interval I. In this paper, we construct k-times continuously differentiable ZFIFs with variable scaling functions on I. Some properties like the positivity, monotonicity, and convexity of a zipper fractal function and the one-sided approximation for a continuous function by a zipper fractal function are studied. The existence of Schauder basis of zipper fractal functions for the space of k-times continuously differentiable functions and the space of p-integrable functions for p ∈ [1,∞) are studied. We introduce the zipper versions of full Müntz theorem for continuous function and p-integrable functions on I for p ∈ [1,∞).
{"title":"Zipper Fractal Functions with Variable Scalings","authors":".. Vi̇jay, A. Chand","doi":"10.31197/atnaa.1149689","DOIUrl":"https://doi.org/10.31197/atnaa.1149689","url":null,"abstract":"Zipper fractal interpolation function (ZFIF) is a generalization of fractal interpolation function through an improved version of iterated function system by using a binary parameter called a signature. The signature allows the horizontal scalings to be negative. ZFIFs have a complex geometric structure, and they can be non-differentiable on a dense subset of an interval I. In this paper, we construct k-times continuously differentiable ZFIFs with variable scaling functions on I. Some properties like the positivity, monotonicity, and convexity of a zipper fractal function and the one-sided approximation for a continuous function by a zipper fractal function are studied. The existence of Schauder basis of zipper fractal functions for the space of k-times continuously differentiable functions and the space of p-integrable functions for p ∈ [1,∞) are studied. We introduce the zipper versions of full Müntz theorem for continuous function and p-integrable functions on I for p ∈ [1,∞).","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"392 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81733774","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}
{"title":"NONEXISTENCE RESULTS FOR SEMI-LINEAR MOORE-GIBSON-THOMPSON EQUATION WITH NON LOCAL OPERATOR","authors":"Hakem Ali, S. Georgiev","doi":"10.31197/atnaa.947937","DOIUrl":"https://doi.org/10.31197/atnaa.947937","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82601953","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}
{"title":"On Solving SDEs with linear coefficients and application to stochastic epidemic models","authors":"Youssef El-Khatib, Q. Al‐Mdallal","doi":"10.31197/atnaa.948300","DOIUrl":"https://doi.org/10.31197/atnaa.948300","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73361115","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}
{"title":"Fixed points of $rho$-nonexpansive mappings using MP iterative process","authors":"Anju Panwar, R. -, Santosh Kumar","doi":"10.31197/atnaa.980093","DOIUrl":"https://doi.org/10.31197/atnaa.980093","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"73 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89430667","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}
The present study focusses on the existence of positivity of the solutions to the higher order three-point boundary value problems involving $p$-Laplacian $$[phi_{p}(x^{(m)}(t))]^{(n)}=g(t,x(t)),~~t in [0, 1],$$ $$ begin{aligned} x^{(i)}(0)=0, &text{~for~} 0leq ileq m-2, x^{(m-2)}(1)&-alpha x^{(m-2)}(xi)=0, [phi_{p}(x^{(m)}(t))]^{(j)}_{text {at} ~ t=0}&=0, text{~for~} 0leq jleq n-2, [phi_{p}(x^{(m)}(t))]^{(n-2)}_{text {at} ~ t=1}&-alpha[phi_{p}(x^{(m)}(t))]^{(n-2)}_{text {at} ~ t=xi}=0, end{aligned} $$ where $m,ngeq 3$, $xiin(0,1)$, $alphain (0,frac{1}{xi})$ is a parameter. The approach used by the application of Guo--Krasnosel'skii fixed point theorem to determine the existence of positivity of the solutions to the problem.
{"title":"Existence of Positivity of the Solutions for Higher Order Three-Point Boundary Value Problems involving p-Laplacian","authors":"Ravi Sankar, Sreedhar Namburi, K. Rajendra Prasad","doi":"10.31197/atnaa.845044","DOIUrl":"https://doi.org/10.31197/atnaa.845044","url":null,"abstract":"The present study focusses on the existence of positivity of the solutions to the higher order three-point boundary value problems involving $p$-Laplacian $$[phi_{p}(x^{(m)}(t))]^{(n)}=g(t,x(t)),~~t in [0, 1],$$ $$ begin{aligned} x^{(i)}(0)=0, &text{~for~} 0leq ileq m-2, x^{(m-2)}(1)&-alpha x^{(m-2)}(xi)=0, [phi_{p}(x^{(m)}(t))]^{(j)}_{text {at} ~ t=0}&=0, text{~for~} 0leq jleq n-2, [phi_{p}(x^{(m)}(t))]^{(n-2)}_{text {at} ~ t=1}&-alpha[phi_{p}(x^{(m)}(t))]^{(n-2)}_{text {at} ~ t=xi}=0, end{aligned} $$ where $m,ngeq 3$, $xiin(0,1)$, $alphain (0,frac{1}{xi})$ is a parameter. The approach used by the application of Guo--Krasnosel'skii fixed point theorem to determine the existence of positivity of the solutions to the problem.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"125 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80379840","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}
{"title":"Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order","authors":"Rabah Djemiat, Bilal Basti, Noureddine Benhamidouche","doi":"10.31197/atnaa.1031436","DOIUrl":"https://doi.org/10.31197/atnaa.1031436","url":null,"abstract":"","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89769655","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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