• East Asian mathematical journal
• /
• v.24 no.4
• /
• pp.359-368
• /
• 2008

The object of this paper is to establish a unique common fixed point theorem through weak compatibility for a sequence of self-maps satisfying a generalized contractive condition in a generalized Menger space. It improves and generalizes the result of Milovanovic-Arandelovic [2], Vasuki [10] and Sehgal and Bharucha-Reid [8]. All the results presented in this paper are new.

• Korean Journal of Mathematics
• /
• v.30 no.4
• /
• pp.571-592
• /
• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.2
• /
• pp.501-515
• /
• 2024

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.

• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.759-766
• /
• 1995

In this paper, we give equivalent forms of the selection theorem of Ding-Kim-Tan. As applications of the selection theorem of Ding-Kim-Tan, we obtain a fixed point theroem of Gale and Mas-Colell type and establish an equilibrium existence theorem for a qualitative game under suitable assumptions in a locally convex Hausdorff topological vector space.

• Kyungpook Mathematical Journal
• /
• v.59 no.1
• /
• pp.73-82
• /
• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• The Pure and Applied Mathematics
• /
• v.10 no.2
• /
• pp.127-132
• /
• 2003

The object of this paper is to extend and generalize the work of Brosowski ［Fixpunktsatze in der approximationstheorie. Mathematica Cluj 11 (1969), 195-200］, Hicks & Humphries ［A note on fixed point theorems. J. Approx. Theory 34 (1982), 221-225］, Khan & Khan ［An extension of Brosowski-Meinardus theorem on invariant approximation. Approx. Theory Appl. 11 (1995), 1-5］ and Singh ［An application of a fixed point theorem to approximation theory J. Approx. Theory 25 (1979), 89-90; Application of fixed point theorem in approximation theory. In: Applied nonlinear analysis (pp. 389-394). Academic Press, 1979］ in metric spaces having convex structure, and in metric linear spaces having strictly monotone metric.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.277-286
• /
• 2003

In this paper, the Monger Probabilistic n-metric space is presented, some Hex point theorem for set valued mapping are extended to Monger probabilistic n-metric space.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.1021-1034
• /
• 2021

This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.

• Honam Mathematical Journal
• /
• v.32 no.4
• /
• pp.663-673
• /
• 2010

In this paper, we will establish common fixed point for compatible mappings of type(${\alpha}$) for four self mappings defined on intuitionistic fuzzy metric space with implicit relations.

• Kyungpook Mathematical Journal
• /
• v.55 no.4
• /
• pp.773-777
• /
• 2015

The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.