Some Fixed Point Theorems for Berinde-Type Contraction Mappings on Gp-Metric Spaces
Şeyma Çevik *
Department of Mathematics, Kahramanmaraş Sütçü İmam University, Kahramanmaraş, 46100, Turkey.
Hasan Furkan
Department of Mathematics, Kahramanmaraş Sütçü İmam University, Kahramanmaraş, 46100, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we define the concepts of (δ, 1 − δ)-weak contraction, (φ , 1 − δ)-weak contraction and Ćirić-type almost contraction in the sense of Berinde in Gp-complete Gp-metric space. Furthermore, we prove the existence of fixed points and common fixed points of mappings satisfying Berinde-type contractions stated above and also provide the conditions which are necessary for the uniqueness of the fixed points and common fixed points. Consequently, we obtain the generalizations of comparable results in the literature. In addition, we introduce a few examples which ensure the existence of these attained results.
Keywords: Fixed point, common fixed point, Gp-metric space, berinde-type almost contractions.