R. K. Verma

Bio: R. K. Verma is an academic researcher. The author has contributed to research in topics: Metric space & Coincidence point. The author has an hindex of 3, co-authored 5 publications receiving 126 citations.

A common fixed point theorem using implicit relation and property (E.A) in metric spaces

Abstract: In this paper, we prove a common fixed point theorem for a quadruple of mappings by using an implicit relation [6] and property (E.A) [1] under weak compatibility. Our theorem improves and generalizes the main Theorems of Popa [6] and Aamri and Moutawakil [1] .Various examples verify the importance of weak compatibility and property (E.A) in the existence of common fixed point and examples are also given to the implicit relation and to validate our main Theorem. We also show that property (E.A) and Meir-Keeler type contractive condition are independent to each other. .

Common Fixed Point Theorems Using Property (E.A) in Complex-Valued Metric Spaces

Abstract: In this paper, we introduce the concept of property (EA) in a complex-valued metric space to prove some common fixed point results for two pairs of weakly compatible mappings, satisfying a contractive condition of ‘max’ type Further, we prove a common fixed point theorem for two pairs of selfmappings satisfying the common limit property in the range of a mapping called (CLR)-property by Sintunavarat and Kumam [Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, J Appl Math, Vol 2011 (2011), Article ID 637958, 14 pages] The related result generalizes various theorems of ordinary metric spaces

A common fixed point theorem of integral type using implicit relation

Abstract: In this paper, we prove a common fixed point theorem for two pairs of weakly compatible mappings in a metric space satisfying a contractive condition of integral type by using an implicit relation of Popa [7] and the property (E.A) introduced recently by Aamri and Mautawakil [1] as a generalization of noncompatible mappings. Our theorem generalizes Theorem 2 of Aamri and Mautawakil in the sense that we can obtain its contractive condition as an special case of our contractive condition. Further, our theorem is a slight variation of Theorem 5 of Popa in the sense that we have replaced the Meir-Keeler type contractive condition to impose the property (E.A). Thus we have unified and generalized both results by using implicit relation and property (E.A) under the integral type mappings.

Weakly compatible mappings and altman type contraction

Abstract: In this paper, a common fixed point theorem for two pairs of weakly compatible mappings satisfying Altman type contraction in metric space is proved. Our result extends and improves several known results.

Fixed Point and Coincidence Point Theorems on Banach Spaces over Topological Semifields and Their Applications

Abstract: We establish some common xed point and coincident point theorems for a quadruple of self-mappings on a Banach space X over a topological semifield. Our first result extends the main result of Pathak et al. [8] to a general class of mappings in which we have dropped the requirement of pairwise commutativity of mappings by imposing certain restrictions on parameters. Our second result deals with the existence of coincidence points for a quadruple of self-mappings under different conditions than in Theorem 1 of [8]. We also discuss an application of our main result to solve certain non-linear function equations in Banach space over a topological semifield.

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Spaces Using (JCLR) Property

Abstract: In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space using the joint common limit in the range property of mappings called (JCLR) property. An example is also furnished which demonstrates the validity of main result. We also extend our main result to two finite families of self mappings. Our results improve and generalize results of Cho et al. [Y. J. Cho, S. Sedghi and N. Shobe, “Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces,” Chaos, Solitons & Fractals, Vol. 39, No. 5, 2009, pp. 2233-2244.] and several known results existing in the literature.

Fixed point theorems in fuzzy metric spaces using property E.A.

Abstract: We prove two common fixed point theorems for a pair of weakly compatible maps in fuzzy metric spaces both in the sense of Kramosil and Michalek and in the sense of George and Veeramani, by using E.A. property.

Common Fixed Point Theorems Using Property (E.A) in Complex-Valued Metric Spaces

Abstract: In this paper, we introduce the concept of property (EA) in a complex-valued metric space to prove some common fixed point results for two pairs of weakly compatible mappings, satisfying a contractive condition of ‘max’ type Further, we prove a common fixed point theorem for two pairs of selfmappings satisfying the common limit property in the range of a mapping called (CLR)-property by Sintunavarat and Kumam [Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space, J Appl Math, Vol 2011 (2011), Article ID 637958, 14 pages] The related result generalizes various theorems of ordinary metric spaces