Nonlinear Contraction Mappings in b-metric Space and Related Fixed Point Results with Application Raji, Muhammed, Kumar Rajpoot, Arvind, Rathour, Laxmi, Narayan Mishra, Lakshmi, Narayan Mishra, Vishnu Transactions on Fuzzy Sets and Systems, 2024 The paper aims to introduce some fixed point results in the setting of sequential compact b-metric spaces to prove Eldeisten-Suzuki-type contraction for self-mappings. These contributions extend the existing literature on fixed point for ordered metric spaces and fixed point theory. Through illustrative examples, we showcase the practical applicability of our proposed notions and results, demonstrating their effectiveness in real-world scenarios.
VARIATIONAL INCLUSION PROBLEM INVOLVING AVERAGED OPERATOR AND ITS CORRESPONDING RESOLVENT-TYPE EQUATION Journal of Nonlinear and Convex Analysis, 2024
Generalized Yosida inclusion problem involving multi-valued operator with XOR operation Javid Iqbal, Yuanheng Wang, Arvind Kumar Rajpoot, Rais Ahmad Demonstratio Mathematica, 2024 In this article, we study a generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation. It is shown that the generalized Yosida variational inclusion problem involving multi-valued operator with XOR operation is equivalent to a fixed point equation. We have proved that the generalized Yosida approximation operator is Lipschitz continuous. Finally, we prove an existence and convergence result for our problem.
Co-Variational Inequality Problem Involving Two Generalized Yosida Approximation Operators Rais Ahmad, Yuanheng Wang, Mohd Ishtyak, Haider Abbas Rizvi, Arvind Kumar Rajpoot Fractal and Fractional, 2023 We focus our study on a co-variational inequality problem involving two generalized Yosida approximation operators in real uniformly smooth Banach space. We show some characteristics of a generalized Yosida approximation operator, which are used in our main proof. We apply the concept of nonexpansive sunny retraction to obtain a solution to our problem. Convergence analysis is also discussed.
Convergence Analysis for Yosida Variational Inclusion Problem with Its Corresponding Yosida Resolvent Equation Problem through Inertial Extrapolation Scheme Arvind Kumar Rajpoot, Mohd Ishtyak, Rais Ahmad, Yuanheng Wang, Jen-Chih Yao Mathematics, 2023 In this paper, we study a Yosida variational inclusion problem with its corresponding Yosida resolvent equation problem. We mention some schemes to solve both the problems, but we focus our study on discussing convergence criteria for the Yosida variational inclusion problem in real Banach space and for the Yosida resolvent equation problem in q-uniformly smooth Banach space. For faster convergence, we apply an inertial extrapolation scheme for both the problems. An example is provided.
H(·,·)-η-ξ-COCOERCIVE OPERATOR WITH AN APPLICATION FOR SOLVING A MIXED VARIATIONAL INCLUSION PROBLEM INVOLVING GENERALIZED CAYLEY OPERATOR IN UNIFORMLY SMOOTH BANACH SPACE Journal of Nonlinear and Convex Analysis, 2023
INERTIAL-TYPE THREE STEP RESOLVENT SCHEME FOR SOLVING CAYLEY INCLUSION PROBLEM Journal of Nonlinear and Convex Analysis, 2023
Solving System of Mixed Variational Inclusions Involving Generalized Cayley Operator and Generalized Yosida Approximation Operator with Error Terms in q-Uniformly Smooth Space Rais Ahmad, Mohd Ishtyak, Arvind Kumar Rajpoot, Yuanheng Wang Mathematics, 2022 In this paper, we solve a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is suggested to discuss the convergence analysis. We have shown that our system admits a unique solution by using the properties of q-uniformly smooth Banach space, and we discuss the convergence criteria for sequences generated by iterative algorithm. Two examples are constructed, and an application is provided.
System of Generalized Variational Inclusions Involving Cayley Operators and XOR-Operation in q-Uniformly Smooth Banach Spaces Javid Iqbal, Arvind Kumar Rajpoot, Monirul Islam, Rais Ahmad, Yuanheng Wang Mathematics, 2022 In this paper, we consider and study a system of generalized variational inclusions involving Cayley operators and an XOR-operation in q-uniformly smooth Banach spaces. To obtain the solution of the system of generalized variational inclusions involving Cayley operators and an XOR-operation, we use some properties of Cayley operators as well as an XOR-operation. We also discuss the convergence criterion. In support of our main result, we provide an example.
Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem Mohammad Akram, Mohammad Dilshad, Arvind Kumar Rajpoot, Feeroz Babu, Rais Ahmad, Jen-Chih Yao Mathematics, 2022 In this paper, we alter Wang’s new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem (SpVIP) in Hilbert space. We discuss the weak convergence for (SpVIP) and strong convergence for the common solution of (SpVIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes.
YOSIDA CAYLEY INCLUSION PROBLEM WITH ITS CORRESPONDING RESOLVENT EQUATION PROBLEM INVOLVING XOR-OPERATION Journal of Nonlinear and Convex Analysis, 2022
