Abstract
New B-𝔘-cyclic weak contraction C-class function concept has been introduced, B-𝔘-cyclic weak F-φ-Φ-contraction types of mapping are defined and the existence of fixed point for such types has been proved. These results mainly generalize fixed point theorems in some previous research papers.
Highlights
First; the class Φ is all non-decreasing mappings φ: [0,∞)→ [0,∞) characterized by φ(t) = 0 if and only if t = 0.Bilgili et al (2014; Karapinar and Sadarangani, 2012; Du and Karapinar, 2013) discussed the concept of Φweakly cyclic contraction mappings and proved fixed point theorems for mappings on Banach spaces
Bilgili et al (2014; Karapinar and Sadarangani, 2012; Du and Karapinar, 2013) discussed the concept of Φweakly cyclic contraction mappings and proved fixed point theorems for mappings on Banach spaces
Many results have been proved in different situations and settings for the purpose of generalization of the Banach contraction principle for contraction mappings and for non-expansive mappings, (Hardy and Rogers, 1973; Gregus, 1980; Kaewcharoen and Kirk, 2006; Kannan, 1971; Kirk, 1965; Park, 1980; Rhoades, 1977; 2001; Sahar Mohamed Ali Abou Bakr, 2013; Wong, 1975; Rhoades, 2009; Ćirić, 2006)
Summary
Bilgili et al (2014; Karapinar and Sadarangani, 2012; Du and Karapinar, 2013) discussed the concept of Φweakly cyclic contraction mappings and proved fixed point theorems for mappings on Banach spaces. It is proved the existence of only one fixed point for such types of mapping for the continuous, one to one and sub-sequentially convergent mapping B. B is U-cyclic Φ-weak contraction on X if and only if there are A∈U and a continuous function φ∈Φ satisfying the two conditions:
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