Jñānābha‎, Vol. 51 (1) (2021), (68-73)

SOME FIXED POINT THEOREMS FOR (F, t)-CONTRACTIVE MAPPINGS ON INCOMPLETE METRIC SPACES


By

Deepak Khantwal* ¹, U. C. Gairola² , Gopi Prasad³ and A. Chauhan

¹,Department of Mathematics, Graphic Era Hill University,

Dehradun-248002, Uttarakhand, India

²Department of Mathematics, H.N.B. Garhwal University

BGR Campus, Pauri Garhwal-246001, Uttarakhand, India

³Department of Mathematics, H.N.B. Garhwal University

Birla Campus, Srinagar(Garhwal)-246174, Uttarakhand, India

Email:deepakkhantwal15@gmail.com*1, ucgairola@rediffmail.com², gopiprasad12@gmail.com³, ahichauhangolu@gmail.com

(Received: December 03, 2020; Revised: December 15, 2020; In final form : March 23, 2021)


Abstract

In this paper, we introduce the notion of a new type of contractive mappings and prove some fixed point results for such mappings in ordered metric spaces. Our results generalize the recent developments of Rashid et al. (Journal of Function Spaces, 2019 (2019), 1-6), which guarantees the existence of a fixed point in such cases wherein the Banach contraction principle, theorem (Proc. Amer. Math. Soc., 132 (2004), 1435-1443) and other fixed point theorems in the literature remain silent. We also provide an affirmative answer to one of the open problems posed by Rashid et al. in the paper mentioned above by relaxing the assumption of continuity to some weaker condition of continuity.


2010 Mathematics Subject Classifications: 47H10, 54H25.

Keywords and phrases: Fixed Point, Ordered metric space, Contraction maps, Orbitally continuous maps


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