New Results for Weakly Compatible (WC) and R-Weakly Commuting (RWC) Mappings with an Applicationin Dynamic Programming

Penumarthy Parvateesam Murthy; Sanjay Kumar; Rajesh Kumar; Pusplata Sahu; Zoran D. Mitrović; Reny George

doi:10.3390/fractalfract6120733

New Results for Weakly Compatible (WC) and R-Weakly Commuting (RWC) Mappings with an Applicationin Dynamic Programming

Penumarthy Parvateesam Murthy
, Sanjay Kumar
, Rajesh Kumar
, Pusplata Sahu
, Zoran D. Mitrović
, Reny George

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The aim of this paper is to obtain some new results about common fixed points. Our results use weaker conditions than those previously used. We have relaxed the conditions for commutating pair mappings and compatible mappings of the type (Formula presented.), which were introduced in 1976. The theorems are enriched by using the concept of (Formula presented.) and various types of weakly commuting pairs of maps in metric spaces. To discuss the existence and uniqueness of the common solutions, we have obtained an application to the functional equations in dynamic programming.

Original language	English
Article number	733
Journal	Fractal and Fractional
Volume	6
Issue number	12
DOIs	https://doi.org/10.3390/fractalfract6120733
State	Published - Dec 2022

Keywords

R-weakly commuting (RWC) mappings
dynamic programming (DP)
weak contraction
weakly compatible (WC) mappings

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10.3390/fractalfract6120733

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title = "New Results for Weakly Compatible (WC) and R-Weakly Commuting (RWC) Mappings with an Applicationin Dynamic Programming",

abstract = "The aim of this paper is to obtain some new results about common fixed points. Our results use weaker conditions than those previously used. We have relaxed the conditions for commutating pair mappings and compatible mappings of the type (Formula presented.), which were introduced in 1976. The theorems are enriched by using the concept of (Formula presented.) and various types of weakly commuting pairs of maps in metric spaces. To discuss the existence and uniqueness of the common solutions, we have obtained an application to the functional equations in dynamic programming.",

keywords = "R-weakly commuting (RWC) mappings, dynamic programming (DP), weak contraction, weakly compatible (WC) mappings",

author = "Murthy, \{Penumarthy Parvateesam\} and Sanjay Kumar and Rajesh Kumar and Pusplata Sahu and Mitrovi{\'c}, \{Zoran D.\} and Reny George",

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T1 - New Results for Weakly Compatible (WC) and R-Weakly Commuting (RWC) Mappings with an Applicationin Dynamic Programming

AU - Murthy, Penumarthy Parvateesam

AU - Kumar, Sanjay

AU - Kumar, Rajesh

AU - Sahu, Pusplata

AU - Mitrović, Zoran D.

AU - George, Reny

PY - 2022/12

Y1 - 2022/12

N2 - The aim of this paper is to obtain some new results about common fixed points. Our results use weaker conditions than those previously used. We have relaxed the conditions for commutating pair mappings and compatible mappings of the type (Formula presented.), which were introduced in 1976. The theorems are enriched by using the concept of (Formula presented.) and various types of weakly commuting pairs of maps in metric spaces. To discuss the existence and uniqueness of the common solutions, we have obtained an application to the functional equations in dynamic programming.

AB - The aim of this paper is to obtain some new results about common fixed points. Our results use weaker conditions than those previously used. We have relaxed the conditions for commutating pair mappings and compatible mappings of the type (Formula presented.), which were introduced in 1976. The theorems are enriched by using the concept of (Formula presented.) and various types of weakly commuting pairs of maps in metric spaces. To discuss the existence and uniqueness of the common solutions, we have obtained an application to the functional equations in dynamic programming.

KW - R-weakly commuting (RWC) mappings

KW - dynamic programming (DP)

KW - weak contraction

KW - weakly compatible (WC) mappings

UR - https://www.scopus.com/pages/publications/85144674268

U2 - 10.3390/fractalfract6120733

DO - 10.3390/fractalfract6120733

M3 - Article

AN - SCOPUS:85144674268

SN - 2504-3110

VL - 6

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 12

M1 - 733

ER -

New Results for Weakly Compatible (WC) and R-Weakly Commuting (RWC) Mappings with an Applicationin Dynamic Programming

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Keywords

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