Tripled Fixed Point Theorems of Caristi type Contraction in Partially Ordered Metric Space

The main aim of this paper is to obtain a unique common tripled fixed point theorem in partial ordered metric space using Caristi type contraction.

BEST PROXIMITY AND COUPLED BEST PROXIMITY POINTS OF ( psi-phi-theta )-ALMOST WEAKLY CONTRACTIVE MAPS IN PARTIALLY ORDERED METRIC SPACE

In this paper we obtain some best proximity point results using almost contractive condition with three control functions (in which two of them need not be continuous) in partially ordered metric spaces. As an application, we prove coupled best proximity theorems. The results presented in this paper generalize the results of Choudhury, Metiya, Postolache and Konar [8]. We draw several corollaries and give illustrative examples to demonstrate the validity of our results.

A Tripled Fixed Point Theorem in Partially Ordered Complete S-Metric Space

Sedghiet al.(Mat. Vesn. 64(3):258-266, 2012) introduced the notion of anS-metric as a generalized metric in 3-tuples S:X3→[0,∞), whereXis a nonempty set. In this paper we prove a tripled fixed point theorem for mapping having the mixed monotone property in partially ordered S-metric space. Our result generalize the result of Savitri and Nawneet Hooda (Int. J. Pure Appl. Sci. Technol. 20(1):111-116, 2014, On tripled fixed point theorem in partially ordered metric space) into the settings of S-metric space.

COMMON FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTION IN PARTIALLY ORDERED METRIC SPACE

In this paper we prove some common fixed point theorems for two and four self-mappings using rational type contraction and some newly notified definitions in partially ordered metric space. In this way we generalized, modify, and extend some recent results due to Chandok and Dinu [14], Shantanwi and Postolache[28] and many others [1, 2, 4, 5, 21, 29, 30], thus generalizing results of Cabrea, Harjani and Sadarangani [12] as well as Dass and Gupta [15]Â in the context of partial order metric setting.

Fixed points for α-ψ-Suzuki contractions with applications to integral equations

Recently, Suzuki [Proc. Amer. Math. Soc. 136 (2008), 1861–1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterized the metric completeness. Paesano and Vetro [Topology Appl., 159 (2012), 911–920] proved an analogous fixed point result on a partial metric space. In this paper we prove some fixed point results for Suzuki-α-ψ-contractions and Suzuki-ϕθ-ψr-contractions on a complete partially ordered metric space. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results.