Fixed Point Theory and Algorithms for Sciences and Engineering
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Solving an integral equation via generalized controlled fuzzy metrics
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2022 - Trang 1-13 - 2022
The purpose of this manuscript is to obtain some fixed point results in
generalized controlled fuzzy metric spaces. Our results generalize and extend
many of the previous findings in the same approach. Moreover, two examples to
support our theorems are obtained. Finally, to examine and strengthen the
theoretical results, the existence and uniqueness of the solution to a nonlinear
integral equation...
Self-adaptive forward–backward splitting algorithm for the sum of two monotone operators in Banach spaces
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2022 - Trang 1-16 - 2022
In this work, we prove the weak convergence of a one-step self-adaptive
algorithm to a solution of the sum of two monotone operators in 2-uniformly
convex and uniformly smooth real Banach spaces. We give numerical examples in
infinite-dimensional spaces to compare our result with some existing algorithms.
Finally, our results extend and complement several existing results in the
literature.
Circumcentering approximate reflections for solving the convex feasibility problem
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2022 - Trang 1-30 - 2022
The circumcentered-reflection method (CRM) has been applied for solving convex
feasibility problems. CRM iterates by computing a circumcenter upon a
composition of reflections with respect to convex sets. Since reflections are
based on exact projections, their computation might be costly. In this regard,
we introduce the circumcentered approximate-reflection method (CARM), whose
reflections rely o...
A self-adaptive extragradient method for fixed-point and pseudomonotone equilibrium problems in Hadamard spaces
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2023 - Trang 1-22 - 2023
In this work, we study a self-adaptive extragradient algorithm for approximating
a common solution of a pseudomonotone equilibrium problem and fixed-point
problem for multivalued nonexpansive mapping in Hadamard spaces. Our proposed
algorithm is designed in such a way that its step size does not require
knowledge of the Lipschitz-like constants of the bifunction. Under some
appropriate conditions,...
Strongly regular points of mappings
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2021 - Trang 1-13 - 2021
In this paper, we use a robust lower directional derivative and provide some
sufficient conditions to ensure the strong regularity of a given mapping at a
certain point. Then, we discuss the Hoffman estimation and achieve some results
for the estimate of the distance to the set of solutions to a system of linear
equalities. The advantage of our estimate is that it allows one to calculate the
coeff...
Nonlinear analysis in p-vector spaces for single-valued 1-set contractive mappings
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2022 - Trang 1-61 - 2022
The goal of this paper is to develop some fundamental and important nonlinear
analysis for single-valued mappings under the framework of p-vector spaces, in
particular, for locally p-convex spaces for $0 < p \leq 1$ . More precisely,
based on the fixed point theorem of single-valued continuous condensing mappings
in locally p-convex spaces as the starting point, we first establish best
approximati...
A remark on Secelean–Wardowski’s fixed point theorems
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2022 - Trang 1-7 - 2022
In this paper we give a simple proof of three fixed point theorems of Secelean
and Wardowski by using the fixed point result of Jachymski et al. Our result is
established with weaker assumptions than the three theorems. Furthermore, the
recent result of Secelean et al. in the setting of a complete metric space can
be also deduced by our theorem.
New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2021 - Trang 1-20 - 2021
We propose Tseng’s extragradient methods for finding a solution of variational
inequality problems associated with pseudomonotone vector fields in Hadamard
manifolds. Under standard assumptions such as pseudomonotone and Lipschitz
continuous vector fields, we prove that any sequence generated by the proposed
methods converges to a solution of variational inequality problem, whenever it
exits. More...
Existence of common fixed point in Kannan F-contractive mappings in quasi-partial b-metric space with an application
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2022 - Trang 1-19 - 2022
The purpose of this study is to demonstrate results on fixed point theory in
quasi-partial b-metric space recognizing a new type of mapping, which is a blend
of F-contraction and Kannan contraction, and to establish the fixed point
results in F-expanding type mappings. Additionally, the obtained results are the
application of the contractive mappings to functional equations. Furthermore,
Mathemati...
Split monotone variational inclusion with errors for image-feature extraction with multiple-image blends problem
Fixed Point Theory and Algorithms for Sciences and Engineering - Tập 2023 - Trang 1-34 - 2023
In this paper, we introduce a new iterative forward–backward splitting algorithm
with errors for solving the split monotone variational inclusion problem of the
sum of two monotone operators in real Hilbert spaces. We suggest and analyze
this method under some mild appropriate conditions imposed on the parameters
such that another strong convergence theorem for this problem is obtained. We
also ap...
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