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Recently, Jleli and Samet [J. Inequal. Appl. (2014), 2014:38] introduced and studied a new contraction to prove a generalization of the Banach contraction principle. In this paper, we introduce the concept of $${\alpha}$$ - $${H\Theta}$$ -contraction with respect to a general family of functions H and we establish Jleli-Samet-type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki-type fixed point results for $${H\Theta}$$ -contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized $${\Theta}$$ -contractions. Moreover, we present an illustrative example to highlight the obtained improvements. [ABSTRACT FROM AUTHOR]

In this paper, we extend the p-metric space to an M-metric space, and we shall show that the definition we give is a real generalization of the p-metric by presenting some examples. In the sequel we prove some of the main theorems by generalized contractions for getting fixed points and common fixed points for mappings. [ABSTRACT FROM AUTHOR]

We introduce the concept of triangular ηc-admissible mappings (pair of mappings) with respect to nc nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular αc-admissible mappings (pair of mappings) with respect to ηc nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given [ABSTRACT FROM AUTHOR]

In this paper, first we introduce the notion of a Gm-Meir-Keeler contractive mapping and establish some fixed point theorems for the Gm-Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a Gcm-Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(α,ψ)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]