Research Article Inequalities on Generalized Sasakian Space Forms Najma Abdul Rehman, 1 Abdul Ghaffar , 2 Esmaeil Abedi, 3 Mustafa Inc , 4,5,6 and Mohammed K. A. Kaabar 7,8,9 1 Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus, Pakistan 2 Department of Mathematics, Ghazi University, D. G. Khan 33200, Pakistan 3 Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, Tabriz, Iran 4 Department of Computer Engineering, Biruni University, 34025 Istanbul, Turkey 5 Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey 6 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan 7 Gofa Camp, Near Gofa Industrial College and German Adebabay, Nifas Silk-Lafto, 26649 Addis Ababa, Ethiopia 8 Jabalia Camp, United Nations Relief and Works Agency (UNRWA), Palestinian Refugee Camp, Gaza Strip Jabalia, State of Palestine 9 Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia Correspondence should be addressed to Mustafa Inc; minc@firat.edu.tr and Mohammed K. A. Kaabar; mohammed.kaabar@wsu.edu Received 16 May 2021; Accepted 27 August 2021; Published 22 September 2021 Academic Editor: Wasim Ul-Haq Copyright © 2021 Najma Abdul Rehman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we find the second variational formula for a generalized Sasakian space form admitting a semisymmetric metric connection. Inequalities regarding the stability criteria of a compact generalized Sasakian space form admitting a semisymmetric metric connection are established. 1. Introduction The harmonic maps have aspects from both Riemannian’s geometry and analysis. Harmonic mappings are considered a vast field, and because of the minimization of energy due to its dual nature, it has many applications in the field of mathematics, physics, relativity, engineering, geometry, crys- tal liquid, surface matching, and animation. Some particular examples of harmonic maps are geodesics, immersion, and solution of the Laplace equation. In physics, p-harmonic maps were studied in image processing. Exponential har- monic maps were discussed in the field of gravity. Due to generalized properties, F-harmonic maps have many applica- tions in cosmology. Harmonic maps have played a significant role in Finsler’s geometry. On complex manifolds, we have interesting and useful outcomes of harmonic maps (for details, see [1, 2]). During the past years, harmonicity on almost contact metric manifolds has been considered a parallel to complex manifolds ([3–5]). The identity map on a Riemannian man- ifold with a compact domain becomes a trivial case of the harmonicity. However, the stability and second variation theory are complex and remarkable here. In [6], a Laplacian upon functions with its first eigenvalue is used to explain sta- bility on Einstein’s manifolds. From [7, 8], we know about the stability-based classification of a Riemannian that simply connected irreducible spaces with a compact domain. From [6], we know a well-known result about the stabil- ity of S 2n+1 . Further in [5], identity map stability upon a compact domain of the Sasakian space form was explained by Gherge et al. (see also [9]). Considering the generalization of Sasakian space forms, Alegre et al. presented the general- ized Sasakian space forms [10]. Therefore, we naturally study the identity map stability upon a compact domain of Hindawi Journal of Function Spaces Volume 2021, Article ID 2161521, 6 pages https://doi.org/10.1155/2021/2161521