• Nonlinear Functional Analysis and Applications
• /
• 제26권5호
• /
• pp.1105-1114
• /
• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• Nonlinear Functional Analysis and Applications
• /
• 제28권1호
• /
• pp.237-249
• /
• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.

• Kyungpook Mathematical Journal
• /
• 제62권1호
• /
• pp.69-88
• /
• 2022

In this work, the three-step intermixed iteration for two finite families of nonlinear mappings is introduced. We prove a strong convergence theorem for approximating a common fixed point of a strict pseudo-contraction and strictly pseudononspreading mapping in a Hilbert space. Some additional results are obtained. Finally, a numerical example in a space of real numbers is also given and illustrated.

• 대한수학회보
• /
• 제21권2호
• /
• pp.55-60
• /
• 1984

In [2], D. Downing and W.A. Kirk obtained a number of fixed point theorems for set-valued maps in matric and Banach spaces. The authors considered maps which are more general than the contractions with nonempty and closed mapping values, and obtain results for maps satisfying certain "inwardness" conditions. A key aspect of their approach is the application of a general fixed point theorem due to Caristi [1]. On the other hand, in [6], the present author obtained a number of equivalent formulations of the well-known result of I. Ekeland [3, 4] on the variational principle for approximate solutions of minimization problems. Some of such formulations include sharpened forms of the Caristi theorem. In this paper, using one of such formulations, we show that Theorems 1-3 and Corollaries 1-5 of [2] are substantially improved by giving geometric estimations of fixed points.ed points.

• 대한수학회논문집
• /
• 제24권1호
• /
• pp.41-55
• /
• 2009

A general common fixed point theorem for two pairs of weakly compatible mappings using an implicit function is proved without any continuity requirement which generalizes the result due to Popa [20, Theorem 3]. In process, several previously known results due to Fisher, Kannan, Jeong and Rhoades, Imdad and Ali, Imdad and Khan, Khan, Shahzad and others are derived as special cases. Some related results and illustrative examples are also discussed. As an application of our main result, we prove an existence theorem for the solution of simultaneous Hammerstein type integral equations.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제26권4호
• /
• pp.215-231
• /
• 2019

In this paper, we establish some ĆIRIC type fixed point theorems in α-complete and orbitally T-complete non-Archimedean modular metric spaces. Meanwhile, we present an illustrative example to emphasis the realized improvements. These obtained results extend and improve certain well known results in the literature.

• Kyungpook Mathematical Journal
• /
• 제48권3호
• /
• pp.367-377
• /
• 2008

In this paper, we give some fixed point theorems for multivalued maps satisfying an implicit relation on metrically convex spaces. Our results extend and generalize some fixed point theorem in the literature.

• 대한수학회지
• /
• 제39권1호
• /
• pp.51-60
• /
• 2002

Some random fixed point theorems for nonexpansive and *-nonexpansive random operators defined on convex and star-shaped sets in a Frechet space are proved. Our work extends recent results of Beg and Shahzad and Tan and Yaun to noncontinuous multivalued random operators, sets analogue to an earlier result of Itoh and provides a random version of a deterministic fixed point theorem due to Singh and Chen.

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.265-278
• /
• 2012

In this work we have considered several common fixed point results in metric spaces for weak compatible mappings. By applications of these results we establish some fixed point theorems in fuzzy metric spaces.

• Journal of applied mathematics & informatics
• /
• 제30권5_6호
• /
• pp.729-740
• /
• 2012

In this paper, we prove common fixed point theorems for occasionally weakly compatible maps in Menger spaces with a continuous t-norm of H-type. As application to our results, we obtain the corresponding fixed point theorems in metric spaces. Our results improve and generalize many known results in Menger spaces as well as in metric spaces.