TY - JOUR AU - Zheng, Dingwei AU - Wang, Pei PY - 2017 TI - Weak \(\theta-\phi-\)contraction and discontinuity JO - Journal of Nonlinear Sciences and Applications SP - 2318--2323 VL - 10 IS - 5 AB - In this paper, we introduce the notion of weak \(\theta-\phi-\)contraction ensuring a convergence of successive approximations but does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised by Rhoades in [B. E. Rhoades, Fixed point theory Appl, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, 72 (1988), 233–245]. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.05.04 DO - 10.22436/jnsa.010.05.04 ID - Zheng2017 ER - TY - JOUR TI - A remark on discontinuity at fixed point AU - R. K. Bisht AU - R. P. Pant JO - J. Math. Anal. Appl. PY - 2017 DA - 2017// VL - 445 ID - Bisht2017 ER - TY - JOUR TI - Fixed point theorems for Reich type contractions on metric spaces with a graph AU - F. Bojor JO - Nonlinear Anal. PY - 2012 DA - 2012// VL - 75 ID - Bojor2012 ER - TY - JOUR TI - Common fixed points of almost generalized contractive mappings in ordered metric spaces AU - L. Ćirić AU - M. Abbas AU - R. Saadati AU - N. Hussain JO - Appl. Math. Comput. PY - 2011 DA - 2011// VL - 217 ID - Ćirić2011 ER - TY - JOUR TI - A new generalization of the Banach contraction principle AU - M. Jleli AU - B. Samet JO - J. Inequal. Appl. PY - 2014 DA - 2014// VL - 2014 ID - Jleli2014 ER - TY - JOUR TI - Some results on fixed points, II AU - R. Kannan JO - Amer. Math. Monthly PY - 1969 DA - 1969// VL - 76 ID - Kannan1969 ER - TY - JOUR TI - Discontinuity and fixed points AU - R. P. Pant JO - J. Math. Anal. Appl. PY - 1999 DA - 1999// VL - 240 ID - Pant1999 ER - TY - JOUR TI - Some fixed point theorems concerning F-contraction in complete metric spaces AU - H. Piri AU - P. Kumam JO - Fixed Point Theory Appl. PY - 2014 DA - 2014// VL - 2014 ID - Piri2014 ER - TY - JOUR TI - A fixed point theorem in partially ordered sets and some applications to matrix equations AU - A. C. M. Ran AU - M. C. B. Reurings JO - Proc. Amer. Math. Soc. PY - 2003 DA - 2003// VL - 132 ID - Ran2003 ER - TY - JOUR TI - A comparison of various definitions of contractive mappings AU - B. E. Rhoades JO - Trans. Amer. Math. Soc. PY - 1977 DA - 1977// VL - 226 ID - Rhoades1977 ER - TY - JOUR TI - Contractive definitions and continuity AU - B. E. Rhoades JO - Fixed point theory and its applications, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI PY - 1988 DA - 1988// VL - 72 ID - Rhoades1988 ER - TY - JOUR TI - New fixed point theorem under R-contractions AU - A. F. Roldán-López de Hierro AU - N. Shahzad JO - Fixed Point Theory Appl. PY - 2015 DA - 2015// VL - 2015 ID - Hierro2015 ER - TY - JOUR TI - Fixed point theorems for \(\alpha\psi\) -contractive type mappings AU - B. Samet AU - C. Vetro AU - P. Vetro JO - Nonlinear Anal. PY - 2012 DA - 2012// VL - 75 ID - Samet2012 ER - TY - JOUR TI - A new type of fixed point theorem in metric spaces AU - T. Suzuki JO - Nonlinear Anal. PY - 2009 DA - 2009// VL - 71 ID - Suzuki2009 ER - TY - JOUR TI - Fixed points of a new type of contractive mappings in complete metric spaces AU - D. Wardowski JO - Fixed Point Theory Appl. PY - 2012 DA - 2012// VL - 2012 ID - Wardowski2012 ER - TY - JOUR TI - New fixed point theorems for \(\theta-\phi-\)contraction in complete metric spaces AU - D.-W. Zheng AU - Z.-Y. Cai AU - P. Wang JO - PY - Preprint DA - Preprint// VL - ID - ZhengPreprint ER -