Coupled Coincidence Point Theorems For Some Weak-contractive Mappings

In2012, Samet et al have proposed a new α weak-contractive condition and provedexistence of fixed points. Later, Mursaleen et al have extended Samet’s findings and obtainedthe existence of coupled fixed points. Motivated by the on-going results, we have proposed anew weak-contractive condition with weak-contractive property, and proved existence resultsof coupled coincidence point. Moreover, we have corrected these gaps in some papers. Ourresults have generated results of corresponding literatures.This paper mainly divided three chapters. In G-metric pace，couple coincidence pointfor α weak-contractive mapping and couple coincidence point for α-φ-weak-contractivemapping are discussed in detail.The first chapter is introduction, introducing G-metric pace and the related conclusion.It mainly introduces the development of couple coincidence point in the latest literature, andsome important research results.The second chapter firstly introduces the related knowledge of α weak-contractivemapping, then the related conclusion in the related literature, finally its spreading, and dis-cusses the existence of couple coincidence point in G-metric pace for α weak-contractivemapping.The third chapter firstly introduces the definition of couple coincidence point forα-φ-weak-contractive mapping. In G-metric pace, the theorem of couple coincidencepoint for α-φ-weak-contractive mapping have been improved, which are spread by thepredominant scholars.At the same time, some proved important lemmas are given, which arevery important in this paper, but also of great value in some papers related to fixed pointproblem.