scholarly journals Existence and Uniqueness of Zeros for Vector-Valued Functions with K-Adjustability Convexity and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 809
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Existence And Uniqueness ◽  
Existence Theorems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Uniqueness Theorems ◽  
New Concepts ◽  
Vector Valued Functions ◽  
Vector Valued

In this paper, we introduce the new concepts of K-adjustability convexity and strictly K-adjustability convexity which respectively generalize and extend the concepts of K-convexity and strictly K-convexity. We establish some new existence and uniqueness theorems of zeros for vector-valued functions with K-adjustability convexity. As their applications, we obtain existence theorems for the minimization problem and fixed point problem which are original and quite different from the known results in the existing literature.

scholarly journals New Existence Results for Fixed Point Problem and Minimization Problem in Compact Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Weng-Seng Heng ◽  
Wei-Shih Du ◽  
Chi-Lin Yen
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Theorems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Convexity Property ◽  
Linear Spaces ◽  
Compact Metric Spaces

We first present some new existence theorems for fixed point problem and minimization problem in compact metric spaces without assuming that mappings possess convexity property. Some applications of our results to new fixed point theorems for nonself mappings in the setting of strictly convex normed linear spaces and usual metric spaces are also given.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

scholarly journals Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1554 ◽  
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Fixed Point Problem ◽  
Comparison Theorems ◽  
Point Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

scholarly journals Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 743 ◽  
Author(s):  
Hossein Fazli ◽  
HongGuang Sun ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Langevin Equation ◽  
Existence And Uniqueness ◽  
Initial Conditions ◽  
Representation Formula ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Contraction Mapping Theorem ◽  
Fractional Langevin Equation ◽  
Fractional Orders

We consider the nonlinear fractional Langevin equation involving two fractional orders with initial conditions. Using some basic properties of Prabhakar integral operator, we find an equivalent Volterra integral equation with two parameter Mittag–Leffler function in the kernel to the mentioned equation. We used the contraction mapping theorem and Weissinger’s fixed point theorem to obtain existence and uniqueness of global solution in the spaces of Lebesgue integrable functions. The new representation formula of the general solution helps us to find the fixed point problem associated with the fractional Langevin equation which its contractivity constant is independent of the friction coefficient. Two examples are discussed to illustrate the feasibility of the main theorems.

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