New inequalities for strongly exponentially generalized functions with applications

Artion Kashuri; Rozana Liko

Ayuda

New inequalities for strongly exponentially generalized functions with applications

Kashuri, Artion ^[1] ; Liko, Rozana ^[1]
1. [1] University Ismail Qemali.
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 1, 2022, págs. 275-300
Idioma: inglés
DOI: 10.22199/issn.0717-6279-3641
Enlaces
- Texto completo
Resumen
- The aim of this paper is to introduce a new class of functions called strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$.Some new integral inequalities of trapezium-type for strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$ functions with modulus $c$ via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$ functions with modulus $c$ via general fractional integrals are obtained. We show that the strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$ functions with modulus $c$ includes several other classes of functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.
Referencias bibliográficas
- G. Alirezaei and R. Mathar, “On exponentially concave functions and their impact in information theory”, 2018 Information Theory and Applications...
- T. Antczak, “(p, r)-invex sets and functions”, Journal of mathematical analysis and applications, vol. 263, no. 2, pp. 355–379, 2001. https://doi.org/10.1006/jmaa.2001.7574
- T. Antczak, “Mean value in invexity analysis”, Nonlinear analysis: theory, methods and applications, vol. 60, no. 8, pp. 1473–1484, 2005....
- S. M. Aslani, M. R. Delavar and S. M. Vaezpour, “Inequalities of fejer type related to generalized convex functions”, International journal...
- M. U. Awan, M. A. Noor, and K. I. Noor, “Hermite-Hadamard inequalities for exponentially convex functions”, Applied mathematics and information...
- F. X. Chen and S. H. Wu, “Several complementary inequalities to inequalities of Hermite-Hadamard type for S-convex functions”, Journal of...
- Y.-M. Chu, M. A. Khan, T. U. Khan, and T. Ali, “Generalizations of hermite-hadamard type inequalities for MT-convex functions”, Journal of...
- M. Rostamian Delavar and M. De La Sen, “Some generalizations of hermite–hadamard type inequalities”, SpringerPlus, vol. 5, no. 1, 2016. https://doi.org/10.1186/s40064-016-3301-3
- S. S. Dragomir, “On some new inequalities of Hermite-Hadamard type for m -convex functions”, Tamkang journal of mathematics, vol. 33, no....
- T. S. Du, M. U. Awan, A. Kashuri, and S. Zhao, “Some K-fractional extensions of the trapezium inequalities through generalized relative semi-(m,h)-preinvexity”,...
- T.-S. Du, J.-G. Liao, and Y.-J. Li, “Properties and integral inequalities of hadamard- Simpson type for the generalized (s, m) -preinvex functions”,...
- M. Jleli, “On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function”, Journal of nonlinear...
- J. Hristov, “Response functions in linear viscoelastic constitutive equations and related fractional operators”, Mathematical modelling of...
- U. N. Katugampola, “New approach to a generalized fractional integral”, Applied mathematics and computation, vol. 218, no. 3, pp. 860–865,...
- A. Kashuri and R. Liko, “Some new Hermite-Hadamard type inequalities and their applications”, Studia scientiarum mathematicarum hungarica,...
- T. Lara, N. Merentes, R. Quintero and E. Rosales, “On strongly m-convex functions”, Mathematica aeterna, vol. 5, no. 3, pp. 521-535, 2015.
- T. Lara, N. Merentes, R. Quintero and E. Rosales, “On inequalities of Fejer and Hermite-Hadamard types for strongly m-convex functions”, Mathematica...
- W. Liu, W. Wen, and J. Park, “Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals”,...
- C. Luo, T. S. Du, M. A. Khan, A. Kashuri and Y. Shen, “Some k-fractional integrals inequalities through generalized λφm-MT-preinvexity”, Journal...
- M. Matłoka, “Inequalities for H-preinvex functions”, Applied mathematics and computation, vol. 234, pp. 52–57, 2014. https://doi.org/10.1016/j.amc.2014.02.030
- M. V. Mihai, “Some Hermite-Hadamard type inequalities obtain via Riemann-Liouville fractional calculus”, Tamkang journal of mathematics, vol....
- M. Matłoka, “Inequalities for H-preinvex functions”, Applied mathematics and computation, vol. 234, pp. 52–57, 2014. https://doi.org/10.1016/j.amc.2014.02.030
- M. V. Mihai, “Some Hermite-Hadamard type inequalities obtain via Riemann-Liouville fractional calculus”, Tamkang journal of mathematics, vol....
- K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, New York: Wiley, 1993.
- M. A. Noor, “Some new classes of non convex functions”, Nonlinear functional analysis and applications, vol. 11, no. 1, pp. 165-171, 2006.
- M. A. Noor and K. I. Noor, “Strongly exponentially convex functions and their properties”, Journal of advanced mathematical studies, vol....
- M. A. Noor and K. I. Noor, “Strongly exponentially convex functions”, UPB scientific bulletin, series a: applied mathematics and physics,...
- M. A. Noor and K. I. Noor, “Exponential convex functions”, Preprint.
- M. A. Noor and K. I. Noor and S. Rashid, “Fractal exponential convex functions and inequalities”, Preprint.
- M. A. Noor and K. I. Noor and S. Rashid, “Exponential r-convex functions and inequalities”, Preprint.
- O. Omotoyinbo and A. Mogbodemu, “Some new Hermite-Hadamard integral inequalities for convex functions”, International journals of science...
- M. E. Özdemir, S. S. Ragomir, and Ç. Yildiz, “The Hadamard inequality for convex function via fractional integrals”, Acta mathematica scientia,...
- J. Pečarić and J. Jakšetić, “Exponential convexity, Euler-Radau expansions and stolarsky means”, Rad Hrvatske akademije znanosti i umjetnosti...
- C. Peng, C. Zhou, C. and T. S. Du, “Riemann-Liouville fractional Simpson’s inequalities through generalized (m, h1, h2)-preinvexity”, Italian...
- R. K. Raina, “On generalized Wright’s hypergeometric functions and fractional calculus operators”, East asian mathematics journal, vol. 21,...
- S. Rashid, M. A. Noor, and K. I. Noor, “Fractional exponentially m- convex functions and inequalities”, International Journal of Analysis...
- M. A. F. dos Santos, “Fractional Prabhakar derivative in diﬀusion equation with non-static stochastic resetting”, Physics, vol. 1, no. 1,...
- M. Z. Sarikaya and F. Ertuğral, “On the generalized Hermite- Hadamard inequalities”, Annals of the University of Craiova, Mathematics and...
- M. Z. Sarikaya and H. Yildirim, “On generalization of the Riesz potential”, Indian journal of mathematical sciences, vol. 3, no. 2, pp. 231-235,...
- H. Wang, T. S. Du and Y. Zhang, “k-fractional integral trapezium- like inequalities through (h, m)-convex and (α, m)-convex mappings”, Journal...
- Y. Zhang, T. S. Du, H. Wang, Y. J. Shen, and A. Kashuri, “Extensions of diﬀerent type parameterized inequalities for generalized (m, h)- preinvex...