Fixed Point Theorems with PPF Dependence for (α, β)-F Contraction in Razumikhin Class
Resumen
In this paper, we provide a novel idea of (α, β)-F contractive, weak (α, β)-F contractive
and generalized (α, β)-F contractive nonself mappings. We establish the existence of fixed
point results with PPF dependence in Razumikhin class. Some examples are also provided to
support our conclusions.
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Citas
[1] Abbas, M. and Nazir, T. Common fixed point of a power graphic contraction pair in partial
metric spaces endowed with graph. Fixed Point Theory Appl. 2013.
[2] Agarwal, R.P., Hussain, N. and Taoudi, M.A. Fixed point theorems in ordered Banach spaces
and applications to nonlinear integral equations. Abstr. Appl. Anal. 2012.
[3] Agarwal, R.P., Kumam, P. and Sintunavarat, W. PPF dependent fixed point theorems for
an αc-admissible nonself-mapping in the Razumikhin class. Fixed Point Theory Appl. 2013.
[4] Ahmad, A.G.B., Fadail, Z., Nashine, H.K., Kadelburg, Z. and Radenovi´c, S. Some new
common fixed point results through generalized altering distances on partial metric spaces.
Fixed Point Theory Appl. 2012.
[5] Babu, G., Satyanarayana, G., and Vinod Kumar, M. (2019). Properties of razumikhin class
of functions and ppf dependent fixed points of weakly contractive type maps. Bull. Int. Math.
Virtual Inst, 9(1), 65-72.
[6] Bernfeld, S.R., Lakshmikatham, V. and Reddy, Y.M. Fixed point theorems of operators with
PPF dependence in Banach spaces. Appl. Anal., 6, 271–280, 1977.
[7] Chandok, S. Some fixed point theorems for (α, β)-admissible Geraghty type contractive
mappins and related results. Math Sci. 2015.
[8] Cho, Y. J., Rassias, T. M., Salimi, P., and Turinici, M. Some PPF dependent fixed point
theorems for new contractions in Banach spaces. Preprint, 1(2.5), 2-6, 2014.
[9] Jachymski, J. The contraction principle for mappings on a metric space with a graph. Proc.
Am. Math. Soc., 136, 1359–1373, 2008.
[10] Karapinar, E. and Samet, B. Generalized (α − ψ) contractive type mappings and related
fixed point theorems with applications. Abstr. Appl. Anal. 2012.
[11] Kutbi, M.A., Hussain, N. and Khaleghizadeh, S. New PPF dependent fixed point theorems
for Suzuki type GF-contractions. Jounal of Fiunction Spaces. 2015.
[12] Kutbi, M.A. and Sintunavarat, W. On sufficient conditions for the existence of past-presentfuture dependent fixed point in the Razumikhin class and application. Abstr. Appl. Anal.
2014.
[13] Samet, B., Vetro, C. and Vetro, P. Fixed point theorem for α−ψ contractive type mappings.
Nonlinear Anal., 75, 2154–2165, 2012.
[14] Salimi, P., Latif, A. and Hussain, N. Modified α−ψ-contractive mappings with applications.
Fixed Point Theory Appl. 2013.
[15] Salimi, P., Vetro, C. and Vetro, P. Fixed point theorems for twisted (α, β) − ψ-contractive
type mappings and applications., 27, 605–615, 2013.
[16] Wardowski, D. Fixed points of a new type of contractive mappings in complete metric spaces.
Fixed PoinT Theory Appl. 2012.
metric spaces endowed with graph. Fixed Point Theory Appl. 2013.
[2] Agarwal, R.P., Hussain, N. and Taoudi, M.A. Fixed point theorems in ordered Banach spaces
and applications to nonlinear integral equations. Abstr. Appl. Anal. 2012.
[3] Agarwal, R.P., Kumam, P. and Sintunavarat, W. PPF dependent fixed point theorems for
an αc-admissible nonself-mapping in the Razumikhin class. Fixed Point Theory Appl. 2013.
[4] Ahmad, A.G.B., Fadail, Z., Nashine, H.K., Kadelburg, Z. and Radenovi´c, S. Some new
common fixed point results through generalized altering distances on partial metric spaces.
Fixed Point Theory Appl. 2012.
[5] Babu, G., Satyanarayana, G., and Vinod Kumar, M. (2019). Properties of razumikhin class
of functions and ppf dependent fixed points of weakly contractive type maps. Bull. Int. Math.
Virtual Inst, 9(1), 65-72.
[6] Bernfeld, S.R., Lakshmikatham, V. and Reddy, Y.M. Fixed point theorems of operators with
PPF dependence in Banach spaces. Appl. Anal., 6, 271–280, 1977.
[7] Chandok, S. Some fixed point theorems for (α, β)-admissible Geraghty type contractive
mappins and related results. Math Sci. 2015.
[8] Cho, Y. J., Rassias, T. M., Salimi, P., and Turinici, M. Some PPF dependent fixed point
theorems for new contractions in Banach spaces. Preprint, 1(2.5), 2-6, 2014.
[9] Jachymski, J. The contraction principle for mappings on a metric space with a graph. Proc.
Am. Math. Soc., 136, 1359–1373, 2008.
[10] Karapinar, E. and Samet, B. Generalized (α − ψ) contractive type mappings and related
fixed point theorems with applications. Abstr. Appl. Anal. 2012.
[11] Kutbi, M.A., Hussain, N. and Khaleghizadeh, S. New PPF dependent fixed point theorems
for Suzuki type GF-contractions. Jounal of Fiunction Spaces. 2015.
[12] Kutbi, M.A. and Sintunavarat, W. On sufficient conditions for the existence of past-presentfuture dependent fixed point in the Razumikhin class and application. Abstr. Appl. Anal.
2014.
[13] Samet, B., Vetro, C. and Vetro, P. Fixed point theorem for α−ψ contractive type mappings.
Nonlinear Anal., 75, 2154–2165, 2012.
[14] Salimi, P., Latif, A. and Hussain, N. Modified α−ψ-contractive mappings with applications.
Fixed Point Theory Appl. 2013.
[15] Salimi, P., Vetro, C. and Vetro, P. Fixed point theorems for twisted (α, β) − ψ-contractive
type mappings and applications., 27, 605–615, 2013.
[16] Wardowski, D. Fixed points of a new type of contractive mappings in complete metric spaces.
Fixed PoinT Theory Appl. 2012.
Publicado
2025-12-06
Número
Sección
Research Articles
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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