Pub Date : 2021-05-23DOI: 10.22771/NFAA.2021.26.02.03
Anupam Das, B. Hazarika, H. Nashine, J. Kim
We proposed to give some new ψ − coupled fixed point theorems using simulation function coupled with other control functions in a complete partially ordered metric space which includes many related results. Further we prove the existence of solution of a fractional integral equation by using this fixed point theorem and explain it with the help of an example.
{"title":"ψ−COUPLED FIXED POINT THEOREM VIA SIMULATION FUNCTIONS IN COMPLETE PARTIALLY ORDERED METRIC SPACE AND ITS APPLICATIONS","authors":"Anupam Das, B. Hazarika, H. Nashine, J. Kim","doi":"10.22771/NFAA.2021.26.02.03","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.02.03","url":null,"abstract":"We proposed to give some new ψ − coupled fixed point theorems using simulation function coupled with other control functions in a complete partially ordered metric space which includes many related results. Further we prove the existence of solution of a fractional integral equation by using this fixed point theorem and explain it with the help of an example.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43214933","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 : 2021-05-23DOI: 10.22771/NFAA.2021.26.02.12
A. Adamu, Jitsupa Deepho, A. Ibrahim, A. Abubakar
In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.
{"title":"APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS","authors":"A. Adamu, Jitsupa Deepho, A. Ibrahim, A. Abubakar","doi":"10.22771/NFAA.2021.26.02.12","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.02.12","url":null,"abstract":"In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43686489","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 : 2021-02-24DOI: 10.22771/NFAA.2021.26.01.14
Bounmy Khaminsou, Chatthai Thaiprayoon, W. Sudsutad, Sayooj Aby Jose
In this paper, we investigate existence, uniqueness and four different types of Ulam’s stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers- Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and Krasnosel’ski i’s fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.
{"title":"QUALITATIVE ANALYSIS OF A PROPORTIONAL CAPUTO FRACTIONAL PANTOGRAPH DIFFERENTIAL EQUATION WITH MIXED NONLOCAL CONDITIONS","authors":"Bounmy Khaminsou, Chatthai Thaiprayoon, W. Sudsutad, Sayooj Aby Jose","doi":"10.22771/NFAA.2021.26.01.14","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.14","url":null,"abstract":"In this paper, we investigate existence, uniqueness and four different types of Ulam’s stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers- Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and Krasnosel’ski i’s fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46518789","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 : 2021-02-24DOI: 10.22771/NFAA.2021.26.01.12
Sehie Park
In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumban, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrovic-Hussain-Sen-Radenovic on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.
{"title":"BEST APPROXIMATIONS FOR MULTIMAPS ON ABSTRACT CONVEX SPACES","authors":"Sehie Park","doi":"10.22771/NFAA.2021.26.01.12","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.12","url":null,"abstract":"In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumban, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrovic-Hussain-Sen-Radenovic on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43995620","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 : 2021-02-24DOI: 10.22771/NFAA.2021.26.01.13
Abed Al-Rahman M. Malkawi, A. Talafhah, W. Shatanawi
n this paper, we introduce the modification of a generalized (Ψ , L ) − weak contraction and we prove some coincidence point results for self-mappings G,T and S, and some fixed point results for some maps by using a ( c ) − comparison function and a comparison function in the sense of a b -metric space.
{"title":"COINCIDENCE AND FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTION MAPPING ON b-METRIC SPACES","authors":"Abed Al-Rahman M. Malkawi, A. Talafhah, W. Shatanawi","doi":"10.22771/NFAA.2021.26.01.13","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.13","url":null,"abstract":"n this paper, we introduce the modification of a generalized (Ψ , L ) − weak contraction and we prove some coincidence point results for self-mappings G,T and S, and some fixed point results for some maps by using a ( c ) − comparison function and a comparison function in the sense of a b -metric space.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48998794","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 : 2021-02-23DOI: 10.22771/NFAA.2021.26.01.11
Soon-Mo Jung, Byungbae Kim
Recently we investigated a type of Hyers-Ulam stability of the Schrodinger equation with the symmetric parabolic wall potential that efficiently describes the quantum harmonic oscillations. In this paper we study a type of Hyers-Ulam stability of the Schrodinger equation when the potential barrier is a quartic wall in the solid crystal models.
{"title":"APPROXIMATE SOLUTIONS OF SCHRÖDINGER EQUATION WITH A QUARTIC POTENTIAL","authors":"Soon-Mo Jung, Byungbae Kim","doi":"10.22771/NFAA.2021.26.01.11","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.11","url":null,"abstract":"Recently we investigated a type of Hyers-Ulam stability of the Schrodinger equation with the symmetric parabolic wall potential that efficiently describes the quantum harmonic oscillations. In this paper we study a type of Hyers-Ulam stability of the Schrodinger equation when the potential barrier is a quartic wall in the solid crystal models.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45109516","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 : 2021-02-23DOI: 10.22771/NFAA.2021.26.01.05
K. Vijaya, G. Murugusundaramoorthy, N. Cho
The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q − calculus operator associated with exponential function.
本文的主要目的是研究一类用与指数函数相关的q−微积分算子定义的解析函数的多数化问题。
{"title":"MAJORIZATION PROBLEMS FOR UNIFORMLY STARLIKE FUNCTIONS BASED ON RUSCHEWEYH Q-DIFFERENTIAL OPERATOR RELATED WITH EXPONENTIAL FUNCTION","authors":"K. Vijaya, G. Murugusundaramoorthy, N. Cho","doi":"10.22771/NFAA.2021.26.01.05","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.05","url":null,"abstract":"The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q − calculus operator associated with exponential function.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48446424","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 : 2021-02-23DOI: 10.22771/NFAA.2021.26.01.10
H. Nashine, R. Ibrahim, Y. Cho, J. Kim
In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Fi- nally, we give some applications of our results in discrete and functional fractional economic systems.
{"title":"FIXED POINT THEOREMS FOR THE MODIFIED SIMULATION FUNCTION AND APPLICATIONS TO FRACTIONAL ECONOMICS SYSTEMS","authors":"H. Nashine, R. Ibrahim, Y. Cho, J. Kim","doi":"10.22771/NFAA.2021.26.01.10","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.10","url":null,"abstract":"In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Fi- nally, we give some applications of our results in discrete and functional fractional economic systems.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44381434","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 : 2021-02-23DOI: 10.22771/NFAA.2021.26.01.07
Hoonjoo Kim
In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadˇzi c type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.
{"title":"COLLECTIVE FIXED POINTS FOR GENERALIZED CONDENSING MAPS IN ABSTRACT CONVEX UNIFORM SPACES","authors":"Hoonjoo Kim","doi":"10.22771/NFAA.2021.26.01.07","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.07","url":null,"abstract":"In this paper, we present a fixed point theorem for a family of generalized condensing multimaps which have ranges of the Zima-Hadˇzi c type in Hausdorff KKM uniform spaces. It extends Himmelberg et al. type fixed point theorem. As applications, we obtain some new collective fixed point theorems for various type generalized condensing multimaps in abstract convex uniform spaces.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49110560","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 : 2021-02-23DOI: 10.22771/NFAA.2021.26.01.03
N. Nhan, Truong Thi Nhan, L. Ngoc, N. Long
In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.
{"title":"LOCAL EXISTENCE AND EXPONENTIAL DECAY OF SOLUTIONS FOR A NONLINEAR PSEUDOPARABOLIC EQUATION WITH VISCOELASTIC TERM","authors":"N. Nhan, Truong Thi Nhan, L. Ngoc, N. Long","doi":"10.22771/NFAA.2021.26.01.03","DOIUrl":"https://doi.org/10.22771/NFAA.2021.26.01.03","url":null,"abstract":"In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43084980","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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